3x^2-6=0 eching

$$3 { x }^{ 2 } -6=0$$

x uchun yechish

$$x=\sqrt{2}\approx 1,414213562$$

$$x=-\sqrt{2}\approx -1,414213562$$

Kvadrat ildizini topish bo'yicha qadamlar

6 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$3x^{2}=6$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{6}{3}$$

2 ni olish uchun 6 ni 3 ga bo‘ling.

$$x^{2}=2$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{2} x=-\sqrt{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$3x^{2}-6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -6 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-6\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-6\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-6\right)}}{2\times 3}$$

-12 ni -6 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{72}}{2\times 3}$$

72 ning kvadrat ildizini chiqarish.

$$x=\frac{0±6\sqrt{2}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±6\sqrt{2}}{6}$$

x=\frac{0±6\sqrt{2}}{6} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{2}$$

x=\frac{0±6\sqrt{2}}{6} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{2}$$

Tenglama yechildi.

$$x=\sqrt{2} x=-\sqrt{2}$$